Q. If the speed of light ($c$), acceleration due to gravity $(g)$ and pressure $(p)$ are taken as the fundamental quantities, then the dimension of gravitational constant is
A) $c^{2}g^{0}p^{- 2}$
B) $c^{0}g^{2}p^{- 1}$
C) $cg^{3}p^{- 2}$
D) $c^{- 1}g^{0}p^{- 1}$
Explanation
Let $\lbrack G\rbrack \propto c^{x}g^{y}p^{z}$ By substituting the following dimensions: $\lbrack G\rbrack = \left\lbrack M^{- 1}L^{3}T^{- 2} \right\rbrack,\lbrack c\rbrack = \left\lbrack {LT}^{- 1} \right\rbrack,\lbrack g\rbrack = \lbrack{LT}^{- 2\ }\rbrack$ $\lbrack p\rbrack = \left\lbrack ML^{- 1}T^{- 2} \right\rbrack$ and by comparing the powers of both sides we can get $x = 0,y = 2,z = - 1$ $\therefore\lbrack G\rbrack \propto c^{0}g^{2}p^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.